The term kernel is derived from a word that can be traced back to c. 1000 and originally meant a seed (contained within a fruit) or the softer (usually edible) part contained within the hard shell of a nut or stone-fruit. The former meaning is now obsolete. It was first used in mathematics when it was defined for integral equations in which the kernel is known and the other function(s) unknown,...

The problem of packing k vertex-disjoint copies of a graph H into another graph G is NP-complete if H has more than two vertices in some connected component. In the framework of parameterized complexity we analyze a particular family of instances of this problem, namely the packing of stars. We prove that packing k copies of H = K1,s is fixed-parameter tractable and give a quadratic kernel for ...

a kernel $j$ of a digraph $d$ is an independent set of vertices of $d$ such that for every vertex $w,in,v(d),setminus,j$ there exists an arc from $w$ to a vertex in $j.$in this paper, among other results, a characterization of $2$-regular circulant digraph having a kernel is obtained. this characterization is a partial solution to the following problem: characterize circulant digraphs which hav...

We propose a new string kernel based on variable-lengthdon’t-care patterns (VLDC patterns). A VLDC pattern is an element of (Σ∪{⋆})∗, where Σ is an alphabet and ⋆ is the variable-length-don’t-care symbol that matches any string in Σ∗. The number of VLDC patterns matching a given string s of length n is O(2). We present an O(n) algorithm for computing the kernel value. We also propose variations...

Abs t r ac t . Let 7) be a Hermitian symmetric space of tube type, S its Shilov boundary and G the neutral component of the group of bi-holomorphic diffeomorphisms of 7). In the model situation 7) is the Siegel disc, S is the manifold of Lagrangian subspaces and G is the symplectic group. We introduce a notion of transversality for pairs of elements in S, and then study the action of G on the s...

The pricing kernel puzzle concerns the locally increasing empirical pricing kernel, which is inconsistent with a risk-averse representative investor in a single period, single state variable setting. Some recent papers worry that the puzzle is caused simply by the mismatch of backward looking subjective and forward looking risk-neutral distributions of index returns. By using a novel test and f...

Let ps be the convolution kernel of the operator e −sL (see [5, (1.10), (1.11)]). When s > 0, e−sL is the solution operator for the Heisenberg heat equation ∂su = −Lu and ps is called the heat kernel (see [6, (7.30), p. 71]. The goal of this note is to study the analytic continuation of the heat kernel ps. This is interesting from the point of view of the theory of analytic hypoellipticity (see...

Several key computational bottlenecks in machine learning involve pairwise distance computations, including all-nearest-neighbors (finding the nearest neighbor(s) for each point, e.g. in manifold learning) and kernel summations (e.g. in kernel density estimation or kernel machines). We consider the general, bichromatic case for these problems, in addition to the scientific problem of N-body sim...

It is shown that in an infinite-dimensional dually separated second category topological vector space X there does not exist a probability measure μ for which the kernel coincides with X. Moreover, we show that in “good” cases the kernel has the full measure if and only if it is finitedimensional. Also, the problem posed by S. Chevet [5, p. 69] is solved by proving that the annihilator of the k...